Experiment 2: Logistic Regression and Newton’s Method August 29, 2018 1 Description In this exercise, you will use Newton’s Method to implement logistic regression on a classification problem. 2 Data college and 40 students who were not admitted. Each (x(i), y(i)) training example contains a student’s score on two standardized exams and a label of whether the student was admitted. Your task is to build build a binary classification model that estimates college admission chances based on a student’s scores on two exams. In your training data, the first column of your x array represents all Test 1 scores

defined by ωT x + b = 0 (1) where ω ∈ Rn is the outward pointing normal vector, and b is the bias term. The n-dimensional space is separated into two half-spaces H+ = {x ∈ Rn | ωT x + b ≥ 0} and H− = {x ωT x + b < 0} by the hyperplane, such that we can classify a given point x0 ∈ Rn according to sign(ωT x + b). Specifically, given a point x0 ∈ Rn, its label y is defined as y0 = sign(ωT x0 + b), i.e. y0 = � 1, ωT x0 + b ≥ 0 −1, otherwise (2) Given any x0 ∈ Rn, we can calculate the signed distance from x to the hyperplane as d0 = ωT x0 + b ∥ω∥ = � ω ∥ω∥ �T x0 + b ∥ω∥ (3) The sign of the distance

delay, or resource availability (extra hands needed for chopping). Personally, I like full apples. Let’s move on from apples to the digital domain. A popular example of lossless data compression algorithm decompress it on arrival? If so, what would be the ideal tradeoff on how much compression we want v/s how much quality loss can we tolerate? Let us slowly build up to that by exploring how quantization low transmission bandwidth. Figure 2-3: Quantization of sine waves. Let’s dig deeper into its mechanics using an example. Let’s assume we have a variable x which takes a 32-bit floating point value in

hyperplane passes through origin. If not, have a bias term b; we will then need both ω and b to define it b > 0 means moving it parallely along ω (b < 0 means in opposite direction) Feng Li (SDU) SVM December hyperplane based linear classifier defined by ω and b Prediction rule: y = sign(ωTx + b) Given: Training data {(x(i), y(i))}i=1,··· ,m Goal: Learn ω and b that achieve the maximum margin For now, assume data are correctly classified by (ω, b) Zero loss on the training examples (non-zero loss later) Feng Li (SDU) SVM December 28, 2021 4 / 82 Margin Hyperplane: ωTx + b = 0, where ω is the normal vector

此外，在附录中，我们提供了本书所涵盖的大多数数学知识的复习。大多数时候，我们会优先考虑直觉和想 法，而不是数学的严谨性。有许多很棒的书可以引导感兴趣的读者走得更远。Bela Bollobas的《线性分析》 (Bollobás, 1999) 对线性代数和函数分析进行了深入的研究。(Wasserman, 2013) 是一本很好的统计学指南。 如果读者以前没有使用过Python语言，那么可以仔细阅读这个Python教程3。 Pedro Larroy, lgov, ati‐ozgur, Jun Wu, Matthias Blume, Lin Yuan, geogunow, Josh Gardner, Maximilian Böther, Rakib Islam, Leonard Lausen, Abhinav Upadhyay, rongruosong, Steve Sedlmeyer, Ruslan Bara‐ tov Miniconda3-py39_4.12.0-MacOSX-x86_64.sh -b 如果我们使用Linux，假设Python版本是3.9（我们的测试版本），将下载名称包含字符串“Linux”的bash脚 本，并执行以下操作： # 文件名可能会更改 sh Miniconda3-py39_4.12.0-Linux-x86_64.sh -b 接下来，初始化终端Shell，以便我们可以直接运行conda。

R510), 515.65 (or later R515), 525.85 (or later R525), or 530.30 (or later R530). The CUDA driver's compatibility package only supports particular drivers. Thus, users should upgrade from all R418, R440 following key features and enhancements. ‣ PyTorch container image version 23.07 is based on 2.1.0a0+b5021ba. Announcements ‣ Starting with the 23.06 release, the NVIDIA Optimized Deep Learning Framework the Frameworks Support Matrix. Container Version Ubuntu CUDA Toolkit PyTorch TensorRT 23.07 2.1.0a0+b5021ba 23.06 2.1.0a0+4136153 TensorRT 8.6.1.6 23.05 22.04 NVIDIA CUDA 12.1.1 2.0.0 TensorRT 8.6

Events and Probability A sample space S is the set of all possible outcomes of a (conceptual or physical) random experiment Event A is a subset of the sample space S P(A) is the probability that event A called the probability measure of A Kolmogorov axioms Non-negativity: p(A) ≥ 0 for each event A P(S) = 1 σ-additivity: For disjoint events {Ai}i such that Ai � Aj = ∅ for ∀i ̸= j P( ∞ � i=1 Ai) = 122 Sample Space, Events and Probability (Contd.) Some consequences P(∅) = 0 P(A � B) = P(A) + P(B) − P(A � B) P(A¬) = 1 − P(A) Feng Li (SDU) GDA, NB and EM September 27, 2023 5 / 122 Conditional

understanding, tool use, role play, playing as AI agent, etc. 最新版本 Qwen1.5 有以下特点： • 6 种模型规模，包括 0.5B、1.8B、4B、7B、14B 和 72B； • 针对每种尺寸提供基础模型和 Chat 模型，并确保聊天模型按照人类偏好进行校准； • 对基础模型和 Chat 模型的多语言支持 • 基础模型和聊天模型都支持多种语言； transformers 进行推理。请确保已安装了 transformers>=4. 37.0 版本。以下是一个非常简单的代码片段示例，展示如何运行 Qwen1.5-Chat 模型，其中包含 Qwen1. 5-7B-Chat 的实例： from transformers import AutoModelForCausalLM, AutoTokenizer device = "cuda" # the device AutoModelForCausalLM.from_pretrained( "Qwen/Qwen1.5-7B-Chat", torch_dtype="auto", device_map="auto" ) tokenizer = AutoTokenizer.from_pretrained("Qwen/Qwen1.5-7B-Chat") # Instead of using model.chat(), we directly

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_p_k2_=9e74eb6f891d47cfaa6f00b5cb 5f617c https://study.163.com/course/courseMain.h tm?share=2&shareId=480000001847407& courseId=1208894818&_trace_c_p_k2_=8 d1b10e04bd34d69855bb71da65b0549 预览版202112 a_ph = tf.placeholder(tf.float32, name='variable_a') b_ph = tf.placeholder(tf.float32, name='variable_b') # 创建输出端子的运算操作，并命名 c_op = tf.add(a_ph, b_ph, name='variable_c') 创建计算图的过程就类比通过符号建立公式? = ? + 运行初始化操作，完成初始化 # 运行输出端子，需要给输入端子赋值 c_numpy = sess.run(c_op, feed_dict={a_ph: 2., b_ph: 4.}) # 运算完输出端子才能得到数值类型的 c_numpy print('a+b=',c_numpy) 可以看到，在 TensorFlow 中完成简单的2.0 + 4.0加法运算尚且如此繁琐，更别说创建复杂 的神经网络算法有